The pair shared the screen as the title couple in the sitcom Joanie Loves Chachi. Before that, they played the same characters on the classic comedy Happy Days.
"May people remember Erin for her contagious smile, warm heart, and animal loving soul. I always hoped she could find peace in her life. God has you now, Erin," Baio wrote on Facebook.
"My sincere condolences. #ErinMoran #HappyDaysFamily," he tweeted.
Moran, 56, was found dead in Indiana after a 911 call alerted first responders to an unresponsive female. The cause for and time of death are expected to be determined through an autopsy and toxicology tests.